Pavement Thickness — Simplified (AASHTO/CBR Method) mechanism

Model scope

The four vectors are arithmetic verification cases only. Two use the widely tabulated AASHTO 1993 typical coefficients 0.44 for asphalt concrete and 0.14 for granular base; the fourth also verifies the exact NIST/ISO millimetre-to-inch conversion. Because the specification does not identify a jurisdiction, chart edition, calibration constant, logarithm base, or complete AASHTO design procedure, the instrument needs review before implementation.

• The CBR thickness expression t=A·log(ESAL)/sqrt(CBR) is not a uniquely defined AASHTO standard formula; the calibration constant A, its units, and the logarithm base are unspecified.
• AASHTO structural number SN=Σaᵢdᵢ is a separate method from a CBR thickness nomograph and cannot be combined with the CBR expression without explicitly selecting one method.
• The structural-number expression is incomplete for normal AASHTO design because it omits drainage coefficients mᵢ, reliability, standard deviation, serviceability loss, effective subgrade resilient modulus, and the design traffic relationship used to determine required SN.
• The CBR method requires a validated chart, curve fit, or jurisdiction-specific calibration. No digitized table or calibration is supplied, so a unique pavement thickness cannot be verified from the specification alone.
• Layer thickness units are unspecified. AASHTO layer coefficients are conventionally applied with layer thickness in inches; using millimetres without conversion produces a 25.4-fold error.

Units and conventions

• For the illustrative CBR vectors, ESAL is dimensionless and log10 is used; A is explicitly supplied as 100 mm per log10(ESAL)/sqrt(CBR), an illustrative calibration rather than a universal standard.
• CBR is a dimensionless percentage value, used numerically as CBR=5 or CBR=100, not as the fraction 0.05 or 1.00.
• For structural number vectors, dᵢ is in inches and aᵢ is dimensionless; therefore SN is dimensionless.
• The exact conversion 1 in=25.4 mm is used for the unit-conversion vector.
• No interpolation is used in any vector.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "method": "CBR_empirical_fit",
    "CBR": 5,
    "design_ESALs": 1000000,
    "A": 100,
    "A_units": "mm",
    "log_base": 10
  },
  "expected_outputs": {
    "estimated_pavement_thickness_mm": 268.328157
  },
  "reference_data": {
    "calibration_row": {
      "A": 100,
      "units": "mm per [log10(ESAL)/sqrt(CBR)]",
      "source_convention": "Illustrative user-specified calibration; no universal AASHTO table value"
    },
    "logarithm": {
      "base": 10,
      "source_convention": "Widely tabulated standard mathematical convention for common-log pavement curve fits"
    }
  },
  "working": "t = A·log10(ESAL)/sqrt(CBR)\nlog10(1,000,000) = 6\nsqrt(5) = 2.2360679775\nA·log10(ESAL) = 100·6 = 600 mm\n t = 600/2.2360679775 = 268.328157 mm"
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification has multiple failure points: CBR = 0 produces an undefined division, the required fit constant A and logarithm base are unspecified, and no selector or applicability rule distinguishes the CBR thickness formula from the AASHTO structural-number branch.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche7/tranche7-results.json
• BOUNDARY_HAZARD_CATALOG.json